Crossing velocities for an annealed random walk in a random potential

Annealed Deviations of Random Walk in Random Scenery

Let (Zn)n∈N be a d-dimensional random walk in random scenery, i.e., Zn = ∑n−1 k=0 Y (Sk) with (Sk)k∈N0 a random walk in Z d and (Y (z))z∈Zd an i.i.d. scenery, independent of the walk. The walker’s steps have mean zero and some finite exponential moments. We identify the speed and the rate of the logarithmic decay of P( 1 nZn > bn) for various choices of sequences (bn)n in [1,∞). Depending on (b...

Annealed Moment Lyapunov Exponents for a Branching Random Walk in a Homogeneous Random Branching Environment∗

We consider a continuous-time branching random walk on the lattice Z (d ≥ 1) evolving in a random branching environment. The motion of particles proceeds according to the law of a simple symmetric random walk. The branching medium formed of Markov birth-and-death processes at the lattice sites is assumed to be spatially homogeneous. We are concerned with the long-time behavior of the quenched m...

A Random Walk with Exponential Travel Times

Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...

On the Annealed Large Deviation Rate Function for a Multi-Dimensional Random Walk in Random Environment

We derive properties of the rate function in Varadhan’s (annealed) large deviation principle for multi-dimensional, ballistic random walk in random environment, in a certain neighborhood of the zero set of the rate function. Our approach relates the LDP to that of regeneration times and distances. The analysis of the latter is possible due to the i.i.d. structure of regenerations.

Transition from the Annealed to the Quenched Asymptotics for a Random Walk on Random